Set of values of m for which a chord of slope m of the circle x^2 +y^2

1.	Set of values of m for which a chord of slope m of the circle x^2 +y^2 4parabola y^2=4x is
Answer» y^2= 16x comparing this with y^2= 4ax we get focus of this parabola is at (a,0) = (4,0) now focal chord : y = m(x-4) ..................1 m is slope of this chord.... this chord is tangent of (x-6)^2+ y^2= 2 this is equation of circle ... for circle x^2+y^2= a^2 if line is tangent then its equation is given by y = mx +(-)a(1+m^2) for (x-6)^2+ y^2= 2 tangent will be y = m(x-6) +(-)a(1+m^2)^1/2 y = mx - 6m +(-)(2+2m^2)^1/2 ..................2 eq 2 & eq 1 are same line so -4m = -6m +(-)(2+2m^2)^1/2 (equating intercepts) 2m = (2+2m^2)^1/2 m^2= 1 m = +(-) 1therefore possible values for m are +1 & -1

Set of values of m for which a chord of slope m of the circle x^2 +y^2 4parabola y^2=4x is

Answer»

y^2= 16x

comparing this with y^2= 4ax we get

focus of this parabola is at (a,0) = (4,0)

now focal chord : y = m(x-4) ..................1

m is slope of this chord....

this chord is tangent of (x-6)^2+ y^2= 2

this is equation of circle ...

for circle x^2+y^2= a^2 if line is tangent then its equation is given by

y = mx +(-)a(1+m^2)

for (x-6)^2+ y^2= 2 tangent will be

y = m(x-6) +(-)a(1+m^2)^1/2

y = mx - 6m +(-)(2+2m^2)^1/2 ..................2

eq 2 & eq 1 are same line so

-4m = -6m +(-)(2+2m^2)^1/2 (equating intercepts)

2m = (2+2m^2)^1/2

m^2= 1

m = +(-) 1therefore possible values for m are +1 & -1